Open problems

1131 registered problems.

OP-00851 Open

Bounded weakening for constrained invertibility

CO · AIM Open Applied Problems · constrained invertibility problems · interleaving distance · multiparameter persistence

OP-00852 Open

A sharp differing-edge bound for convex plane-tree flips

CO · AIM Open Applied Problems · flip graphs · non-crossing spanning trees

OP-00853 Open

The happy-edge conjecture for convex plane spanning trees

CO · AIM Open Applied Problems · flip graphs · non-crossing spanning trees

OP-00854 Open

Counting cospherical tuples in lattice cubes

CO · AIM Open Applied Problems · cospherical points · incidence geometry · lattice points

OP-00855 Open

Continuous harmonic extension of every degree-zero sphere boundary map

AP · AIM Open Applied Problems · boundary value problems · harmonic maps

OP-00856 Open

Concentration of eikonal entropy production on jump curves

AP · AIM Open Applied Problems · Aviles–Giga functionals · eikonal equations · entropy productions

OP-00857 Open

Approximation preserving a compressible elastic energy

AP · AIM Open Applied Problems · diffeomorphic approximation · nonlinear elasticity · Sobolev homeomorphisms

OP-00858 Open

Radial classification of higher-degree entire planar Ginzburg–Landau vortices

AP · AIM Open Applied Problems · Ginzburg–Landau equation · radial symmetry · vortices

OP-00859 Open

Polynomial growth of every entire minimal graph

AP · AIM Open Applied Problems · Bernstein theorems · minimal graphs

OP-00860 Open

Surjectivity of the two-dimensional Euler endpoint map

AP · AIM Open Applied Problems · diffeomorphism groups · Euler equations · exponential maps

OP-00861 Open

Sustained double-exponential gradient growth on the Euler torus

AP · AIM Open Applied Problems · Euler equations · small-scale creation · vorticity gradients

OP-00862 Open

Sharp vertex bounds for generalized triangulations in even dimensions

GT · AIM Open Applied Problems · face numbers · triangulated manifolds

OP-00863 Open

Steady planar flow around an obstacle at arbitrary Reynolds number

AP · AIM Open Applied Problems · exterior domains · flows past obstacles · stationary Navier–Stokes equations

OP-00864 Open

A strict gap between face and cycle percolation thresholds

PR · AIM Open Applied Problems · continuum percolation · random simplicial complexes

OP-00865 Open

The maximal heat-transfer exponent at finite Prandtl number

AP · AIM Open Applied Problems · Boussinesq equations · Nusselt numbers · Rayleigh–Bénard convection

OP-00866 Open

Best convex shape for insulation of fixed thickness and perimeter

AP · AIM Open Applied Problems · convex sets · shape optimization · thermal insulation

OP-00867 Open

A sharp Betti-number bound for 4-manifold triangulation complexity

GT · 4-manifolds · AIM Open Applied Problems · generalised triangulations · triangulation complexity

OP-00868 Open

Transversal ratio approaching one for simplicial four-polytopes

CO · AIM Open Applied Problems · hypergraph transversals · simplicial polytopes · weak colorings

OP-00869 Open

Three or four layers for 2-degenerate graphs

CO · AIM Open Applied Problems · degenerate graphs · geometric thickness

OP-00870 Open

Arbitrarily large integer-distance sets in general position

MG · AIM Open Applied Problems · Erdős problems · general position · integer distance sets

OP-00871 Open

Existence of a nonaffine polynomial minimal graph

AP · AIM Open Applied Problems · minimal graphs · polynomial solutions

OP-00872 Open

Reconstructing simplicial spheres from facet adjacency

CO · AIM Open Applied Problems · facet-ridge graphs · polytope reconstruction · simplicial spheres

OP-00873 Open

Global classical solutions of the spatially inhomogeneous Landau–Coulomb equation

AP · AIM Open Applied Problems · global classical solutions · kinetic equations · Landau equation

OP-00874 Open

Anomalous viscous dissipation with fixed large-scale forcing

AP · AIM Open Applied Problems · anomalous dissipation · Navier–Stokes equations · turbulence

OP-00875 Open

Stationarity of Lipschitz weak solutions of the minimal-surface system

AP · AIM Open Applied Problems · minimal graphs · weak solutions

OP-00876 Open

Tagged-particle thermalization with an interacting background

AP · AIM Open Applied Problems · Lenard–Balescu equation · mean-field limits · tagged particles

OP-00877 Open

Hardness of minimum-dilation triangulation

MG · AIM Open Applied Problems · geometric spanners · NP-hardness · triangulations

OP-00878 Open

An inertial manifold for the two-dimensional Navier–Stokes flow

AP · AIM Open Applied Problems · global attractors · inertial manifolds · Navier–Stokes equations

OP-00879 Open

Multiplicity one at planar network singularities

AP · AIM Open Applied Problems · curvature flows · planar networks · self-similar shrinkers

OP-00880 Open

Exact diameter of the leaf-slide graph on labelled trees

CO · AIM Open Applied Problems · labelled trees · network realignment complexes · reconfiguration graphs

OP-00881 Open

Uniqueness of the limiting shape at a network singularity

AP · AIM Open Applied Problems · blow-up limits · curvature flows · planar networks

OP-00882 Open

The nonlinear Landau limit of weakly interacting particles

AP · AIM Open Applied Problems · Landau equation · particle systems · weak-coupling limits

OP-00883 Open

Motion-planning complexity of symmetric products of non-orientable surfaces

AT · AIM Open Applied Problems · non-orientable surfaces · symmetric products · topological complexity

OP-00884 Open

Energy conservation at the exact Onsager Hölder exponent

AP · AIM Open Applied Problems · energy conservation · Euler equations · Onsager's conjecture

OP-00885 Open

Wedge-of-spheres structure of path-product matching complexes

CO · AIM Open Applied Problems · categorical products of graphs · matching complexes · wedges of spheres

OP-00886 Open

Improving the exponential lower bound for peeling sequences

CO · AIM Open Applied Problems · convex hulls · peeling sequences · point sets

OP-00887 Open

Planar Rips complexes as wedges of spheres

AT · AIM Open Applied Problems · homotopy types · Vietoris–Rips complexes · wedges of spheres

OP-00888 Open

Connectivity of plane spanning-path reconfiguration

CO · AIM Open Applied Problems · flip graphs · plane spanning paths · reconfiguration

OP-00889 Open

Polynomial anisotropic minimal graphs in dimensions four and five

AP · AIM Open Applied Problems · anisotropic minimal hypersurfaces · Bernstein theorems

OP-00890 Open

Polynomial-size convex difference decompositions

MG · AIM Open Applied Problems · DC decompositions · piecewise linear functions · polyhedral complexes

OP-00891 Open

Polynomial bounds for the graph diameter of polytopes

CO · AIM Open Applied Problems · convex polytopes · graph diameter · Hirsch conjecture

OP-00892 Open

Maximal motion-planning complexity from positive simplicial volume

AT · AIM Open Applied Problems · aspherical manifolds · simplicial volume · topological complexity

OP-00893 Open

Exact motion-planning complexity of real projective spaces

AT · AIM Open Applied Problems · immersions · real projective spaces · topological complexity

OP-00894 Open

The sharp radius in quantitative Steinitz selection

MG · AIM Open Applied Problems · convex hulls · quantitative Steinitz theorems · sparse approximation

OP-00895 Open

A limiting law for maximal persistence in random clique complexes

PR · AIM Open Applied Problems · persistent homology · random clique complexes

OP-00896 Open

Uniqueness of bounded semigeostrophic potential vorticity

AP · AIM Open Applied Problems · optimal transport · semigeostrophic equations · weak solutions

OP-00897 Open

Global smooth evolution of small semigeostrophic perturbations

AP · AIM Open Applied Problems · global smooth solutions · Monge–Ampère equations · semigeostrophic equations

OP-00898 Open

Sierksma's lower bound for Tverberg partitions

MG · AIM Open Applied Problems · Sierksma's conjecture · Tverberg partitions

OP-00899 Open

Eventual classification of simplicial line arrangements

CO · AIM Open Applied Problems · line arrangements · simplicial arrangements

OP-00900 Open

Monotonicity of connectivity in spherical Čech filtrations

AT · AIM Open Applied Problems · Čech complexes · homotopy connectivity · spheres